1. Field of the Invention
The present invention relates to a switching power supply, in particular, to a technology in which a linear control instruction value to use at a moment of transition of a control mode from a non-linear control mode to a linear control mode is predicted and set based on a load current in the non-linear control mode.
2. Description of the Related Art
The DC-DC type switching power supplies have a function of a power converter for obtaining a desired output power from an input power, and are widely used for power supplies to provide power for various electronic devices. The switching power supplies use switching elements as a means for converting and adjusting the power.
ICs (integrated circuits) that are loads on the power supply have recently developed to become high density and highly integrated owing to fine semiconductor processes, and are making progress to a high function, low voltage and high current. With this trend, demand for voltage accuracy of a power supply has become earnest, thus, requiring a power supply with extremely high accuracy.
A highly functioning IC changes a consuming electric current thereof in a broad range. A power supply connecting to a load of such an IC transiently increases and decreases the output voltage with abrupt decrease and increase, respectively, of the current. Still in such a situation, the value of the output voltage of the power supply must be kept in a permissible range. Thus, the power supply needs quick response to the load variation.
Conventionally, a control section of a DC-DC type switching power supply is composed of an analog circuit and uses a control method of a linear feed-back control such as PID control and PI control. Since the conventional linear control restricts the transient characteristics within a bandwidth of a negative feedback loop, quick transient response can be hardly performed. As a result, the adverse effect of the abrupt current variation is suppressed using a huge decoupling capacitor.
In a condition of low voltage and high current, a voltage applied to the IC may rise exceeding the permissible range because of a voltage drop due to wiring impedance between the power supply and the IC and because of a transient voltage variation due to wiring inductance between the power supply and the IC. In order to suppress this situation, a distributed arrangement system is a main stream in which the power supply is disposed at a close proximity of the load IC.
Since the highly functioning load IC has a multiple of data buses and address buses lead out from the IC, it is undesirable to arrange the power supply with a huge decoupling capacitor at close proximity of the IC. Therefore, the power supply needs to perform sufficient quick load response yet with little external decoupling capacitors.
To satisfy the demand, a number of non-patent documents, such as G. Feng, W. Eberle and Y. Liu “A new digital control algorithm to achieve optimal dynamic performance in DC-DC converters” in Proc. IEEE PESC, 2005, pp. 2744-2748, G. Feng, E. Meyer and Y. Liu “High performance digital control algorithms for DC-DC converters based on the principle of capacitor charge balance” in Proc. IEEE PESC, 2006, pp. 1740-1743, E. Meyer and Y. Liu “A quick capacitor charge balance control method to achieve optimal dynamic response for buck converters” in Proc. IEEE PESC, 2007, pp. 1549-1555, and Z. Zhao, V. Smolyakov and A. Prodic “Continuous-time digital signal processing based controller for high-frequency DC-DC converters” in Proc. IEEE APEC, 2007, pp. 882-886, for example, disclose power supplies employing a non-linear control system based on the capacitor charge balance theory.
The non-linear control system changes the controlling quantity corresponding to variation of a deviation not linearly but non-linearly. The controlling quantity is a duty factor or a PWM pulse width for controlling switching elements in a switching power supply.
FIG. 6 shows variation of PWM pulses in a transient period (in a load current varying period) and corresponding variation of the inductor current and the output voltage in the cases of a linear control and a non-linear control.
As shown in the figure, the disclosed power supplies of the non-linear control system operates linearly in the steady state, and in a transient state with voltage variation due to variation of the load current, the control mode is changed over to non-linear control and the power supply operates in the non-linear control scheme.
As described previously, transient characteristics in the linear control mode are restricted within a bandwidth of the feedback loop. Consequently, the controlling quantity (a duty factor or a PWM pulse width) in the linear control mode varies only gradually corresponding to current variation as shown in the figure, resulting in large transient variation of voltage.
On the other hand, the disclosed non-linear control mode gives the maximum controlling quantity (the maximum or minimum PWM pulse width) from the initial moment of the transient period as shown in the figure, allowing control exceeding the bandwidth restriction of the linear control mode. Accordingly, a power supply with good transient performance is obtained. Of the PWM pulses in FIG. 6, the period indicated by “the maximum pulse width” is a pulse of duty factor of 100%, and the period indicated by “the minimum pulse width” is a pulse of duty factor of 0%.
The capacitor charge balance theory mentioned above directs to modeling and analysis of a DC-DC type switching power supply in a steady state, utilizing the condition that the mean value of capacitor current of an output capacitor (flow of charged electric charges or discharged electric charges of the output capacitor) in a single switching period must be zero.
The non-linear control method mentioned above is an expansion of this concept to voltage variation in the transient period. In this non-linear control method, the voltage variation in the transient period is recovered by one time of switching operation as shown in FIG. 6.
To recover a voltage variation in one switching operation, the output voltage must be equal at the start and the end of a switching cycle. For satisfying this condition, an ON period and an OFF period of a PWM pulse are obtained so as to equalize the changed electric charges and the discharged electric charges of the output capacitor, and control is conducted based on those periods. Referring to the waveform in FIG. 6, the control is conducted based on an ON period and an OFF period that equalize the areas Δ1 and Δ2 in FIG. 6. After recovery of the voltage, the control mode is returned to the conventional linear control mode, in which a stable operation is conducted.
The control sections of the power supplies disclosed in the references mentioned above have a construction capable of operating in the both control modes of a linear control mode and a non-linear control mode. Operation is conducted in the linear control mode in the steady state, in the non-linear control mode based on the charge balance theory in the transient state, and again in the linear control mode in the steady state after the end of the transient state. The control section holds, during operation in the non-linear control mode, the controlling quantity (a duty factor or a PWM pulse width) in the steady state at the right before turning into the steady state. Then, operation is conducted again in the linear control mode, using the held controlling quantity to start the linear control.
Patent documents, such as Japanese Unexamined Patent Application Publication No. 2004-304873 and Japanese Unexamined Patent Application Publication No. 2004-304961 disclose other switching power supplies with a digital control scheme having a construction to ensure stable output voltage still in an abrupt change in the load current.
As described above, the control section of the power supplies disclosed in the non-patent documents cited above stores and holds the controlling quantity (a duty factor or a PWM pulse width) in the linear control mode at right before changing over from a linear control mode to a non-linear control mode according to variation of a load current, and is operated to start the linear control again after the operation period of the non-linear control mode using the stored and held controlling quantity just after returning to the linear control mode.
Stating again, the control section stores and holds the controlling quantity in the linearly controlled steady state with a load current before variation, throughout the transient period with a varying load current, and the linear control in the steady state after the transient period is started using the held controlling quantity.
A duty factor of a DC-DC type switching power supply is determined by a ratio of an output voltage to an input voltage in an ideal condition. For a step down type DC-DC converter circuit shown in FIG. 7, for example, the duty factor Ds is represented by the following equation (1) using an input voltage Vin and an output voltage Vout in an ideal condition with no resistive component which would be consisted of an on-resistance in the output switch element S (which can be a MOSFET), an equivalent resistance of the inductor L, and a resistance in the wiring.Ds=Vout/Vin  (1)This duty factor Ds in the ideal condition is a constant value irrespective of the output current.In an actual switching power supply, however, due to existence of a loss caused by the resistance component, the duty factor Ds is different from the duty factor in the ideal condition.
In FIG. 7, Di represents a diode, C represents a capacitor, and R represents a load.
FIG. 8 shows an equivalent circuit of a voltage step down type DC-DC converter (a switching power supply) taking the resistance component into consideration, in particular the equivalent circuit operating at a duty factor Ds in the steady state. In FIG. 8, the on-resistance of the switching element S shown in FIG. 7 is represented by Rds_on1, the on-resistance of the diode Di (or a synchronous rectifying switch replacing the diode Di) is represented by Rds_on2, the equivalent resistance of the inductor L is represented by RL, and the output current (a load current) in the steady state is represented by Is.
Assuming zero values of the resistance Rds_on1, Rds_on2, and RL, the output voltage Vout is represented by the ideal value Ds*Vin based on the relation of equation (1). When the resistances Rds_on1, Rds_on2, and RL are not zero, the output voltage Vout is decreased by an amount due to a voltage drop caused by the resistances.
The output current Is, a load current, is a mean inductor current averaged over the increasing inductor current running in the inductor L with the switch S ON and the decreasing inductor current running in the inductor L with the switch S OFF.
The mean voltage drop ΔV1 when the switch S is ON and the diode Di is OFF is given byΔV1=(Rds_on1+RL)*Is  (2)At this time, a relation Ds*Vin−ΔV1=Vout holds.
On the other hand, the mean voltage drop ΔV2 when the switch S is OFF and the diode Di is ON is given byΔV2=(Rds_on2+RL)*Is  (3)At this time, a relation Ds*V1n−ΔV2=Vout holds.
Therefore, the mean value ΔV of the voltage drop caused by the resistance component averaged over time is given by
                                                                        Δ                ⁢                                                                  ⁢                V                            =                                                Ds                  *                  Δ                  ⁢                                                                          ⁢                  V                  ⁢                                                                          ⁢                  1                                +                                                      (                                          1                      -                      Ds                                        )                                    *                  Δ                  ⁢                                                                          ⁢                  V                  ⁢                                                                          ⁢                  2                                                                                                        =                                                [                                                            Ds                      *                      Rds_on                      ⁢                                                                                          ⁢                      1                                        +                                                                  (                                                  1                          -                          Ds                                                )                                            *                      Rds_on                      ⁢                                                                                          ⁢                      2                                        +                                          R                      L                                                        ]                                *                Is                                                                                        =                              Req                *                Is                                                                        (        4        )            whereinReq=Ds*Rds_on1+(1−Ds)*Rds_on2+RL As a result, the actual output voltage Vout is given by subtracting the time-averaged value ΔV of voltage drop from the ideal output voltage Ds*Vin.Ds*Vin−ΔV=Vout  (5)
The equations (4) and (5) lead to the following equation.Ds*Vin−Req*Is =Vout  (6)
The equation (6) shows that a desired output voltage Vout is obtained by necessarily setting a rather high value of the ideal output voltage Ds*Vin.
As is apparent from equation (6), an actual duty factor Ds of a switching power supply depends not only on the input voltage Vin and the output voltage Vout but also on the resistance component Req and the output current Is.
The duty factor Ds in the steady state varies depending on the load current Is. This duty factor Ds differs from the duty factor Ds in the ideal condition more greatly in a switching power supply with a larger resistance component including the ON resistance in a MOS switch S and an equivalent resistance of an inductance L.
The duty factor Ds in an ideal condition is constant irrespective of variation of the load current (an output current) Is. However, an actual duty factor Ds varies by an amount of ΔDs due to variation ΔIout of the output current.ΔDs=(Req/Vin)*ΔIout  (7)Thus, the variation ΔDs of the duty factor varies in proportion to the variation ΔIout in the output current. When the load driven by the switching power supply is an IC, the variation ΔDs of the duty factor Ds cannot be disregarded with an increased current in the IC.
Because of the above-described facts, the method of conventional technology in which a controlling quantity to be used at a moment of transition from a transient state to a steady state is a controlling quantity before the current varies, is not desirable because the linear control starts with a controlling quantity different from the optimum controlling quantity after the current is varied. Thus, variation of output voltage occurs caused by the deviation from the optimum controlling quantity.
FIG. 9 shows this situation in which the load current Iout (=Is) increases from Iout1 to Iout2 (Iout1<Iout2). In the period the load current Iout 1 is steadily flowing, the switching power supply is in a steady state and operates in a linear control mode. The duty factor Ds1 in this period is given by the following equation (8) using the resistance component Req as in the case of FIG. 8 based on equation (6).Ds1=(Vout/Vin)+(Req/Vin)*Iout1  (8)
When the load current varies from Iout1 to Iout2, the output voltage Vout varies transiently. The control section controls shifting to the non-linear control mode and at the same time stores and holds the duty factor Ds1. When the output voltage Vout recovers the predetermined value owing to the non-linear control, the control section shifts to the linear control mode again and conducts linear control using the held duty factor Ds1. However, the load current at this time is Iout2. The optimum duty factor Ds2 in the period with a steady load current of Iout2 is,Ds2=(Vout/Vin)+(Req/Vin)*Iout2  (9)Thus, Ds1<Ds2 in the case of Iout1<Iout2.
The duty factor Ds1 is smaller than the optimum duty factor Ds2 for Iout2. When the control section starts to control using the duty factor Ds1, the output voltage Vout cannot be kept at a predetermined value corresponding to the load current Iout2, and the output voltage Vout begins to vary as shown in FIG. 9. The control section detects the variation and operates aiming the output voltage at the predetermined value of. However, because the operation is conducted by a linear control mode, the transient performance is restricted by the bandwidth of the feedback loop and the large variation occurs in the output voltage Vout.
Although the patent documents cited above disclose a technology to ensure stable output without oscillation irrespective of increased gain of a control loop, the documents are silent about a technology to cope with the variation of the duty time factor (an error in the controlling quantity) due to the load current and the resistance component.